A calculus for modal compact Hausdorff spaces

被引：0
|
作者：
Bezhanishvili, Nick [1 ]
Carai, Luca [2 ]
Ghilardi, Silvio [2 ]
Zhao, Zhiguang [3 ]
机构：
[1] Univ Amsterdam, Inst Log Language & Computat, NL-1098 XH Amsterdam, Netherlands
[2] Univ Milan, Dept Math, I-20122 Milan, Italy
[3] Taishan Univ, Sch Math & Stat, Tai An 271000, Peoples R China
来源：
JOURNAL OF LOGIC AND COMPUTATION | 2025年
关键词：
modal logic; compact Hausdorff space; continuous relation; de Vries algebra; strict implication; Pi(2)-rule; admissible rule. 2020 Mathematics Subject Classification;
D O I：
10.1093/logcom/exae086
中图分类号：
TP301 [理论、方法];
学科分类号：
081202 ;
摘要：
The symmetric strict implication calculus S(2)ICis a modal calculus for compact Hausdorff spaces. This is established throughde Vries duality, linking compact Hausdorff spaces with de Vries algebras-complete Boolean algebras equipped with aspecial relation. Modal compact Hausdorff spaces are compact Hausdorff spaces enriched with a continuous relation. Thesespaces correspond, via modalized de Vries duality, to upper continuous modal de Vries algebras. In this paper, we introducethe modal symmetric strict implication calculus (MSIC)-I-2, which extends (SIC)-I-2. We prove that MS(2)ICis strongly sound andcomplete with respect to upper continuous modal de Vries algebras, thereby providing a logical calculus for modal compactHausdorff spaces. We also develop a relational semantics for MS(2)ICthat we employ to show admissibility of various Pi(2)-rules in this system
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页数：30
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